# How do you convert an infintesimal generator of a Markov process to a transition function?

Suppose a continuous-time continuous-step Markov stochastic process $X_t$ has infinitesimal generator $\mu(x, t)$, $\sigma(x, t)$ ($\mu$, $\sigma$, and $X_0$ are known). How can we use this information to find a density function for the value of $X_t$ (at some fixed time $t$)?

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Integrate the associated differential equation, if possible. –  mjqxxxx Jan 3 '13 at 5:23